Problem $3$: For steady state optical excitation, we can write the hole diffusion equation as:

For steady state optical excitation, we can write the hole diffusion equation as

$D_p\frac{d^{2}p}{d{x}^2}=\frac{p}{{}_p}-g_{op}$

Assume that a long $p^{+}-n$ diode is uniformly illuminated by an optical signal. resulting in $g_{op}EH\frac{P}{c}{m}^3-$s$.$ Show that the excess hole distribution in the n region is

$p(x_n)=[p_n(e^{qVkT}-1)-g_{op}\frac{L_p^2}{D_p}]e^{-\frac{x_n}{L_p}}+\frac{g_{op}{L}_p^2}{D_p}$